
/* @(#)e_acos.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/* acos(x)
 * Method :
 *	acos(x)  = pi/2 - asin(x)
 *	acos(-x) = pi/2 + asin(x)
 * For |x|<=0.5
 *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
 * For x>0.5
 * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
 *		= 2asin(sqrt((1-x)/2))
 *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
 *		= 2f + (2c + 2s*z*R(z))
 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
 *     for f so that f+c ~ sqrt(z).
 * For x<-0.5
 *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
 *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
 *
 * Special cases:
 *	if x is NaN, return x itself;
 *	if |x|>1, return NaN with invalid signal.
 *
 * Function needed: sqrt
 */

#include "fdlibm.h"

#ifdef _NEED_FLOAT64

static const __float64
    one = _F_64(1.00000000000000000000e+00), /* 0x3FF00000, 0x00000000 */
    pi = _F_64(3.14159265358979311600e+00), /* 0x400921FB, 0x54442D18 */
    pio2_hi = _F_64(1.57079632679489655800e+00), /* 0x3FF921FB, 0x54442D18 */
    pio2_lo = _F_64(6.12323399573676603587e-17), /* 0x3C91A626, 0x33145C07 */
    pS0 = _F_64(1.66666666666666657415e-01), /* 0x3FC55555, 0x55555555 */
    pS1 = _F_64(-3.25565818622400915405e-01), /* 0xBFD4D612, 0x03EB6F7D */
    pS2 = _F_64(2.01212532134862925881e-01), /* 0x3FC9C155, 0x0E884455 */
    pS3 = _F_64(-4.00555345006794114027e-02), /* 0xBFA48228, 0xB5688F3B */
    pS4 = _F_64(7.91534994289814532176e-04), /* 0x3F49EFE0, 0x7501B288 */
    pS5 = _F_64(3.47933107596021167570e-05), /* 0x3F023DE1, 0x0DFDF709 */
    qS1 = _F_64(-2.40339491173441421878e+00), /* 0xC0033A27, 0x1C8A2D4B */
    qS2 = _F_64(2.02094576023350569471e+00), /* 0x40002AE5, 0x9C598AC8 */
    qS3 = _F_64(-6.88283971605453293030e-01), /* 0xBFE6066C, 0x1B8D0159 */
    qS4 = _F_64(7.70381505559019352791e-02); /* 0x3FB3B8C5, 0xB12E9282 */

__float64
acos64(__float64 x)
{
    __float64 z, p, q, r, w, s, c, df;
    __int32_t hx, ix;
    GET_HIGH_WORD(hx, x);
    ix = hx & 0x7fffffff;
    if (ix >= 0x3ff00000) { /* |x| >= 1 */
        __uint32_t lx;
        GET_LOW_WORD(lx, x);
        if (((ix - 0x3ff00000) | lx) == 0) { /* |x|==1 */
            if (hx > 0)
                return _F_64(0.0); /* acos(1) = 0  */
            else
                return pi + _F_64(2.0) * pio2_lo; /* acos(-1)= pi */
        }
        return __math_invalid(x); /* acos(|x|>1) is NaN */
    }
    if (ix < 0x3fe00000) { /* |x| < 0.5 */
        if (ix <= 0x3c600000)
            return pio2_hi + pio2_lo; /*if|x|<2**-57*/
        z = x * x;
        p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
        q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
        r = p / q;
        return pio2_hi - (x - (pio2_lo - x * r));
    } else if (hx < 0) { /* x < -0.5 */
        z = (one + x) * _F_64(0.5);
        p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
        q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
        s = sqrt64(z);
        r = p / q;
        w = r * s - pio2_lo;
        return pi - _F_64(2.0) * (s + w);
    } else { /* x > 0.5 */
        z = (one - x) * _F_64(0.5);
        s = sqrt64(z);
        df = s;
        SET_LOW_WORD(df, 0);
        c = (z - df * df) / (s + df);
        p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
        q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
        r = p / q;
        w = r * s + c;
        return _F_64(2.0) * (df + w);
    }
}

_MATH_ALIAS_d_d(acos)

#endif /* _NEED_FLOAT64 */
